Cut Off Edge Particles?
I was not able to find a way to cut the edges off, but I was able to find a decent substitute: Weight Painting. This is the result I produced:



With your mouse in the 3D viewport, key Tab to enter edit mode. Key W and select Subdivide 3-5 times (the more the better, until it lags to much).

Next, key Tab followed by Ctrl + Tab to enter weight painting mode. Go to the Tools bar. Make sure Weight: is set to 1. Paint a streak down the middle of the lateral faces and a dot on each end by dragging the mouse while holding the left button down. Your result should look something like this (mirrored on the hidden sides):



Note that I moved the emmission time to 5 frames so that I could paint in peace.

Lastly, go to your particle system settings, the Vertex Groups drop down and the Density: option. Select Group (it should be the only group there). Here is the modified .blend file. I might fiddle with the painting and size of the emitted particles to get a nicer looking result.